A small business recorded the number of customer inquiries received per day over six conse… — JAMB UTME

A small business recorded the number of customer inquiries received per day over six consecutive days as follows: $4$ , $7$ , $8$ , $11$ , $13$ , and $17$ . What is the variance of the daily customer inquiries?

Answer: 18

Answer

The variance of the daily customer inquiries is

18

To find the variance of the data set

\{4, 7, 8, 11, 13, 17\}

, first calculate the mean:

\bar{x} = \frac{4+7+8+11+13+17}{6} = 10

. Next, compute the squared deviation of each data point from the mean:

(4-10)^2 = 36

(7-10)^2 = 9

(8-10)^2 = 4

(11-10)^2 = 1

(13-10)^2 = 9

, and

(17-10)^2 = 49

. Summing these squared deviations gives

108

. Dividing this total by the number of observations (

6

) yields a variance of

18

Step-by-Step Solution

Calculate the arithmetic mean of the given data set.

\bar{x} = 10

The mean is required as the central point from which deviations are calculated.

Determine the squared deviation of each data value from the mean.

(-6)^2 = 36

(-3)^2 = 9

(-2)^2 = 4

1^2 = 1

3^2 = 9

7^2 = 49

Variance measures the average squared distance of data points from the mean.

Sum all calculated squared deviations.

\sum (x - \bar{x})^2 = 36 + 9 + 4 + 1 + 9 + 49 = 108

This provides the total sum of squares for the data set.

Divide the total sum of squares by the number of observations (

n = 6

\sigma^2 = \frac{108}{6} = 18

Population variance formula is

\sigma^2 = \frac{\sum (x - \bar{x})^2}{n}

Key Concept

Variance of Ungrouped Data

Estimated Time:1m 30s

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