Test Index

Measures of Central Tendency and Dispersion

Question : 170 of 211

Marks: +1, -0

The SD for the data 6,9,10,3,7 is

Solution:

Concept:

Standard deviation measures the spread of data around the mean.

Explanation:

Step 1: Compute the mean of the data.

Mean =

\frac{6+9+10+3+7}{5} = \frac{35}{5} = 7

Step 2: Find the squared deviations from the mean.

(6-7)^2 = (-1)^2 = 1

(9-7)^2 = 2^2 = 4

(10-7)^2 = 3^2 = 9

(3-7)^2 = (-4)^2 = 16

(7-7)^2 = 0^2 = 0

Step 3: Sum the squared deviations.

Sum =

1 + 4 + 9 + 16 + 0 = 30

Step 4: Divide by the number of data points (population SD).

Variance =

\frac{30}{5} = 6

Step 5: Take the square root.

Standard deviation =

\sqrt{6} \approx 2.449 \approx 2.45

Answer:

2.45

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