[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.13.1″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n
[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” global_colors_info=”{}”]<\/p>\n
Measures of dispersion help us to describe how much spread a data set is. We can define it as the state of data getting scattered, stretched, squeezed or spread out in different categories.<\/span><\/b><\/p>\n In statistics, data dispersion helps us quickly understand the dataset by classifying them into their own specific scattering criteria like variance, ranging, and standard deviation.\u00a0<\/span><\/p>\n <\/span><\/p>\n The measure of dispersion is classified as:<\/span><\/p>\n (i) Absolute measure of dispersion<\/span><\/p>\n (ii) A relative measure of dispersion<\/span><\/p>\n <\/span><\/p>\n This measure of dispersion represents the dispersion of observation in terms of distances. We can express the measure of dispersion in units such as Centimetre, Rupees, kilograms, and more quantities depending on the situation.<\/span><\/p>\n Let\u2019s see the types of the absolute measure of dispersion.<\/span><\/span><\/p>\n Example: 2, 3, 4, 5, 6, 7\u00a0<\/span><\/p>\n Range = (Maximum value \u2013 Minimum value)\u00a0<\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= (7 \u2013 2)\u00a0<\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = 5\u00a0<\/span><\/p>\n <\/span><\/p>\n Example: 1, 2, 3, 4, 5, 6, 7\u00a0<\/span><\/p>\n Mean = (sum of all the values)\/(total number of terms)\u00a0<\/span><\/p>\n \u202f \u202f \u202f \u202f \u202f \u202f \u202f \u202f= (1 + 2 + 3 + 4 + 5 + 6 + 7)\/7\u00a0<\/span><\/p>\n \u202f \u202f \u202f \u202f \u202f \u202f\u00a0 \u00a0= 28\/7<\/span><\/p>\n \u202f \u202f \u202f \u202f \u202f \u202f \u202f \u202f= 4<\/span><\/p>\n <\/p>\n In simple language, it shows how far a value is from the mean of the entire value. For example, we can calculate how far a student\u2019s mark in an exam is from the mean of the whole class using a variance.<\/span><\/p>\n Formula:\u00a0<\/span><\/p>\n \\left(\\sigma^{2}\\right)=\\sum(X-\\mu)^{2} \/ N<\/span><\/span><\/p>\n <\/span><\/p>\n Formula:\u00a0<\/span><\/p>\n Standard Deviation = \u221a\u03c3<\/span><\/p>\n <\/span><\/p>\n \u00a0<\/span><\/p>\n Formula:\u00a0<\/span><\/p>\n Q=(1 \/ 2) \\times\\left(Q_{3}-Q_{1}\\right)<\/span><\/span><\/p>\n <\/span><\/p>\n Formula:\u00a0<\/span><\/p>\n Mean Deviation using Mean:\\sum|X-M| \/ N<\/span><\/span><\/p>\n Mean Deviation using Median: \u2211 |X \u2013 X<\/span>i<\/span>| \/ N\u00a0<\/span><\/p>\n Where X = Mean, M = Median, N= Number of values, X<\/span>i<\/span> = frequency of the ith class interval<\/span><\/p>\n <\/p>\n We compare the distributions of two or more data sets using a relative measure of dispersion. They can be –\u00a0<\/span><\/p>\n Formula:\u00a0 (L \u2013 S) \/ (L + S)<\/span><\/p>\n where L = maximum value\u00a0<\/span><\/p>\n S = minimum value\u00a0<\/span><\/p>\n <\/p>\n Formula:\u00a0<\/span><\/p>\n C.V = (\u03c3 \/ X) \u00d7 100\u00a0<\/span><\/p>\n X = standard deviation\u202f\u00a0<\/span><\/p>\n \u03c3 = mean\u00a0<\/span><\/p>\n <\/p>\n Formula:<\/span><\/p>\n \\sigma=\\left(\\sqrt{\\left(X-X_{1}\\right)}\\right) \/(N-1)<\/span><\/span><\/p>\n Deviation = (X \u2013 X<\/span>1<\/span>)\u202f\u00a0<\/span><\/p>\n \u03c3 = standard deviation\u202f\u00a0<\/span><\/p>\n N= total number\u00a0\u00a0<\/span><\/p>\n <\/p>\n Formula:\u00a0<\/span><\/p>\n \\left(Q_{3}-Q_{1}\\right) \/\\left(Q_{3}+Q_{1}\\right)<\/span><\/span><\/p>\n \\mathrm{Q}_{3}<\/span> <\/span>= Upper Quartile\u202f\u00a0<\/span><\/p>\n Q_{1}<\/span> <\/span>= Lower Quartile\u00a0<\/span><\/p>\n <\/span><\/p>\n Mean Deviation using mean: \u2211 |X \u2013 M| \/ N\u00a0<\/span><\/p>\n Mean Deviation using median: \u2211 |X \u2013 X<\/span>i<\/span>| \/ N\u00a0<\/span><\/p>\n Where, X = Mean, M = Median, N= Number of values, X<\/span>i<\/span> = frequency of the ith class interval<\/span><\/p>\n <\/span><\/p>\n Note –<\/b> Relative measures of dispersion don\u2019t have any units.<\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n <\/span><\/p>\n Maximum value L = 68; Minimum value S =18<\/span><\/p>\n Range R = L \u2212 S = 68 \u221218 = 50<\/span><\/p>\n Formula for coefficient of range = (L \u2013S) \/ (L + S)<\/span><\/p>\n So, Coefficient of range = (68 \u2013 18 ) \/ (68 +18)\u00a0<\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 50\/86<\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 0.581<\/span><\/p>\n <\/p>\n Mean = (1 + 3 + 5 + 6 + 6 + 7 + 8 + 10)\/8\u00a0<\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 46\/ 8<\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 5.75<\/span><\/p>\n <\/span><\/p>\n Now, to calculate the standard deviation,<\/span><\/p>\n Subtract the mean from each individual value<\/span><\/p>\n (1 \u2013 5.75), (3 \u2013 5.75), (5 \u2013 5.75), (6 \u2013 5.75), (6 \u2013 5.75), (7 \u2013 5.75), (8 \u2013 5.75), (10 \u2013 5.75)<\/span><\/p>\n = -4.75, -2.75, -0.75, 0.25, 0.25, 1.25, 2.25, 4.25<\/span><\/p>\n <\/span><\/p>\n Squaring these values we get,\u00a0<\/span><\/p>\n 22.563, 7.563, 0.563, 0.063, 0.063, 1.563, 10.563, 18.063<\/span><\/p>\n <\/span><\/p>\n Adding the above values we get,<\/span><\/p>\n 22.563 + 7.563 + 0.563 + 0.063 + 0.063 + 1.563 + 5.063 + 18.063<\/span><\/p>\n = 55.504<\/span><\/p>\n <\/span><\/p>\n Number of terms (n) = 8<\/span><\/p>\n Therefore, variance \\left(\\sigma^{2}\\right)<\/span><\/span>\u00a0= 55.504\/ 8 = 6.94<\/span><\/p>\n So, Standard deviation (\u03c3) = \u221a 6.94 = 2.63<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\nTypes of Measures of Dispersion<\/b><\/h2>\n
The Absolute Measure of Dispersion<\/b><\/h2>\n
\n
\n
\n
\n
\n
\n
\n
Relative Measures of Dispersion<\/b><\/h2>\n
\n
\n
\n
\n
\n
Examples<\/b><\/h2>\n
\u00a01. Find the range and coefficient of range of the following data: 25, 68, 48, 53, 18, 39, 44.<\/span><\/h3>\n
2. Find the Variance and Standard Deviation of the Following Numbers: 1, 3, 5, 6, 6, 7, 8, 10.<\/span><\/h3>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n