Students from a statistics class were asked to record their height in inches. The heights ( as recorded) were:
65, 72, 68, 64, 60, 55, 73, 71, 52, 63, 61, 74, 69, 67, 74, 50, 4, 75, 67, 62, 66, 80, 64, 65
Find five number summary.
I don't know what five numbers you are seeking, but this might be a partial response.
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.
To find the five-number summary for a set of data, follow these steps:
1. Arrange the data in ascending order.
The given heights, in ascending order, are: 4, 50, 52, 55, 60, 61, 62, 63, 64, 64, 65, 65, 66, 67, 67, 68, 69, 71, 72, 73, 74, 74, 75, 80.
2. Find the minimum value.
The minimum value in this data set is 4.
3. Find the first quartile (Q1).
The first quartile is the median of the lower half of the data. The lower half consists of the values from the minimum up to the median. In this case, the values are: 4, 50, 52, 55, 60, 61, 62, 63, 64, 64, 65. The median of this lower half is 60.
4. Find the median (Q2).
The median is the middle value of the data when arranged in ascending order. In this case, there is an odd number of data points, so the median would be the 12th value, which is 65.
5. Find the third quartile (Q3).
The third quartile is the median of the upper half of the data. The upper half consists of the values from the median up to the maximum. In this case, the values are: 65, 66, 67, 67, 68, 69, 71, 72, 73, 74, 74, 75, 80. The median of this upper half is 71.
6. Find the maximum value.
The maximum value in this data set is 80.
Therefore, the five-number summary for the given heights is:
Minimum: 4
First quartile (Q1): 60
Median (Q2): 65
Third quartile (Q3): 71
Maximum: 80