Chapter F, Problem 1E

To determine

To Answer:

Find the mean, the median, and the mode of the data set $\mathrm{21,28,16,42,38}$.

Answer to Problem 1E

Solution:

Mean of the given data is $29$.

Median of the given data is $28$.

There is no mode.

Explanation of Solution

1. Concept:

Step 1: Find the mean of the given data by finding the sum of the items of the given data and divide it by the number of items.

Step 2: Arrange the data in ascending order. If the number of items is odd, the middle number is the median. If the number of items is even, the mean of the two middle terms is the median.

Step 3: The mode is the number that occurs maximum number of times in the given data set.

2. Calculation:

Mean of a set of numbers is given by the formula, $\stackrel{-}{x}=\frac{\mathrm{S}\mathrm{u}\mathrm{m}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{s}}{\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{ }\mathrm{o}\mathrm{f}\mathrm{ }\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{s}}.$

Sum of items $=21+28+16+42+38=145$.

Number of items $=5$.

To find the mean, divide the sum of items by the number items.

$\stackrel{-}{x}=\frac{145}{5}=29$

Therefore, the mean is 29.

To find the median, arrange the numbers in ascending order and find the middle number.

$\mathrm{16,21,28,38,42}$

The number of items is $5$, which is odd.

The middle number is $28$.

Therefore, the median is $28$.

There is no mode for the given data as no numbers repeat.

Conclusion:

Mean of the given data is $29$.

Median of the given data is 28.

There is no mode for the given data as no numbers repeat.