QuestionFind the min, max, range, mean (to 2 decimals), and standard deviation of TV hours for 24 kids: 77, 38, 35, 54, 30, 32, 85, 12, 70, 91, 25, 71, 95, 90, 99, 11, 66, 74, 90, 78, 34, 77, 39, 62.

Studdy Solution

STEP 1

Assumptions1. The data represents the number of hours spent watching TV last week by a sample of24 children. . We are asked to find the minimum, maximum, range, mean, and standard deviation of the data.
3. The minimum, maximum, and range should be exact values.
4. The mean and standard deviation should be rounded to two decimal places.

STEP 2

First, we need to find the minimum value in the data set. This is the smallest number in the data set.

STEP 3

After examining the data, we find that the minimum value is11.

STEP 4

Next, we need to find the maximum value in the data set. This is the largest number in the data set.

STEP 5

After examining the data, we find that the maximum value is99.

STEP 6

The range of a data set is the difference between the maximum and minimum values. We can calculate the range as follows $Range = Max - Min$

STEP 7

Plug in the values for the maximum and minimum to calculate the range.
$Range =99 -11$

STEP 8

Calculate the range.
$Range =99 -11 =88$

STEP 9

The mean of a data set is the sum of all the values divided by the number of values. We can calculate the mean as follows $Mean = \frac{Sum\, of\, all\, values}{Number\, of\, values}$

STEP 10

First, we need to find the sum of all the values. Add up all the numbers in the data set.

STEP 11

After adding all the numbers, we find that the sum of all the values is,590.

STEP 12

Now, plug in the values for the sum of all values and the number of values to calculate the mean.
$Mean = \frac{,590}{24}$

STEP 13

Calculate the mean and round to two decimal places.
$Mean = \frac{,590}{24} =66.25$

STEP 14

The standard deviation is a measure of how spread out the numbers in the data set are. It is the square root of the variance. First, we need to find the variance. The variance is the average of the squared differences from the mean. We can calculate the variance as follows $Variance = \frac{Sum\, of\, (x_i - Mean)^2}{Number\, of\, values}$

STEP 15

First, we need to find the squared differences from the mean. Subtract the mean from each value, square the result, and then add up all these squared results.

STEP 16

After calculating, we find that the sum of the squared differences from the mean is8,334.58.

STEP 17

Now, plug in the values for the sum of the squared differences from the mean and the number of values to calculate the variance.
$Variance = \frac{,334.58}{24}$

STEP 18

Calculate the variance.
$Variance = \frac{8,334.58}{24} =347.27$

STEP 19

Now, we can find the standard deviation. The standard deviation is the square root of the variance. We can calculate the standard deviation as follows $Standard\, Deviation = \sqrt{Variance}$

STEP 20

Plug in the value for the variance to calculate the standard deviation.
$Standard\, Deviation = \sqrt{347.27}$

STEP 21

Calculate the standard deviation and round to two decimal places.
$Standard\, Deviation = \sqrt{347.27} =18.63$ So, the minimum is11, the maximum is99, the range is88, the mean is66.25, and the standard deviation is18.63.

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