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To calculate the mean and standard deviation from the given frequency distribution, we will use the following formulas:
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2 partsStep-by-step solution
8 stepsTo calculate the mean and standard deviation from the given frequency distribution, we will use the following formulas:
Mean ()
Standard Deviation ()
First, let's create a table to organize the calculations for and .
The total number of students is .
| Hours per day () | Number of students () | |||
|---|---|---|---|---|
| 4 | 5 | 20 | 16 | 80 |
| 5 | 7 | 35 | 25 | 175 |
| 6 | 5 | 30 | 36 | 180 |
| 7 | 9 | 63 | 49 | 441 |
| 8 | 12 | 96 | 64 | 768 |
| 9 | 4 | 36 | 81 | 324 |
| 10 | 3 | 30 | 100 | 300 |
| 11 | 5 | 55 | 121 | 605 |
| Total | 50 | 365 | 2873 |
From the table, we have:
Part a· 3 steps
Mean
Use the formula for the mean.
Substitute the calculated values into the formula.
Calculate the mean.
The mean is 7.30 hours (correct to two decimal places).
Part b
Standard Deviation
Use the formula for the standard deviation.
Substitute the calculated values into the formula.
Perform the division and squaring.
Subtract the values.
Calculate the square root and round to two decimal places.
The standard deviation is 2.04 hours (correct to two decimal places).
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