Question
Asked Sep 23, 2019
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What is the mode of a distribution of scores for a variable measured by?

What is the variance of a distribution of scores for a variable measured by? 

What is the mean of a distribution of scores for a variable measured by? 

What is the standard deviation of a distribution of scores for a variable measured by? 

 

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Expert Answer

Step 1

Let us take a small dataset with frequency distribution and understand all the terms with this example.

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Class Frequency 17-27 18 28-38 42 39-49 68 69 50-60 61-71 78 72-82 68 83-93 22

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Step 2

1) Mode: Mode is the number which is having the highest frequency  in the dataset.

From the above table, the highest frequency is 78. So the class respective to this is 61-71.

2) Mean: Mean is the average of all the numbers.

Calculation of mean

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Calculation of mean Frequency (Fi) Mid-value (Xj) Class FiXi 17-27 18 22 396 33 28-38 42 1386 68 39-49 44 2992 69 55 3795 50-60 78 61-71 66 5148 72-82 77 5236 68 83-93 22 88 1936 Total 365 20889 Mean = X = FiX{ ΣFi 20889 57.23 Mean 365

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Step 3

3) Variance - It is the squared deviation from the center of d...

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ΣΕ (Χ -Χ): Σ-1 112650.7 Variance 309.48 11 365 1 _ Frequency (Fi)Mid-value(X - X) (Xi) F(X-X)2 (Xi-X)2 Class _ 1241.153 17-27 18 22 -35.23 22340.75 28-38 42 33 -24.23 587.0929 24657.9 39-49 68 44 -13.23 175.0329 11902.24 55 343.1301 50-60 69 -2.23 4.9729 5999.206 61-71 78 66 8.77 76.9129 72-82 68 77 19.77 390.8529 26578 946.7929 83-93 22 88 1936 20829.44 Total 112650.7 365 20889

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