We read your photo as:
Calculate the mean, variance, standard deviation, and mode for the given grouped frequency distribution.
Mathematics
ScanSolve AI Answer
Answers
3 partsStep-by-step solution
12 stepsTo compute the mean, variance, standard deviation, and mode for the given grouped frequency distribution, we first need to determine the class mark () for each interval and then calculate the sums required for the formulas.
Here is the table with the necessary calculations:
| Class Interval | Frequency (f) | Class Mark (x) | |||
|---|---|---|---|---|---|
| 0 - 5 | 9 | 2.5 | 22.5 | 6.25 | 56.25 |
| 6 - 11 | 16 | 8.5 | 136.0 | 72.25 | 1156.00 |
| 12 - 17 | 16 | 14.5 | 232.0 | 210.25 | 3364.00 |
| 18 - 23 | 18 | 20.5 | 369.0 | 420.25 | 7564.50 |
| 24 - 29 | 5 | 26.5 | 132.5 | 702.25 | 3511.25 |
| 30 - 35 | 5 | 32.5 | 162.5 | 1056.25 | 5281.25 |
| 36 - 41 | 1 | 38.5 | 38.5 | 1482.25 | 1482.25 |
| Total |
Part a· 3 steps
Mean
Use the formula for the mean of a grouped frequency distribution.
Substitute the calculated sums.
Calculate the mean and round to one decimal place.
The mean is .
Part b
Variance
Use the formula for the variance of a grouped frequency distribution.
Substitute the calculated sums.
Calculate the terms.
Calculate the variance and round to one decimal place.
The variance is .
Part c
Standard Deviation
Use the formula for standard deviation, which is the square root of the variance.
Substitute the calculated variance.
Calculate the standard deviation and round to one decimal place.
The standard deviation is .
Part d· 2 steps
Mode
Identify the modal class, which is the class with the highest frequency.
The highest frequency is 18, corresponding to the class interval 18 - 23.
Identify the
Was this helpful?
Try one yourself
A new problem that tests the same skill.
Still stuck on this one?
Ask a follow-up, and the answer starts from this question.
Got a different question?Ask your own question
More Mathematics Questions
QCalculate the mean, median, and standard deviation for the given grouped frequency distribution.QCalculate the mean, variance, and standard deviation for the given grouped data.QSolve for mean, mode, cumulative frequency, variance, standard deviationQConstruct a grouped frequency distribution table and calculate the mean mark and standard deviation…QCalculate the mean , median ,mode, standard deviation.
Browse by topic:Statistics