Fifty-one (51) statistics students were asked how much sleep they get per school night (rounded to the nearest hour). The results are as shown in the following frequency distribution table. Which percentile is in the 26th position? State your result/answer as value with exactly two digits after the decimal. Values Frequency Cumulative Frequency 4 2 2 5 5 7 6 7 14 7 11 25 8 16 41 9 6 47 10 4 51 25.00 50.00 26.00 50.98 25.50
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Fifty-one (51) statistics students were asked how much sleep they get per school night (rounded to the nearest hour). The results are as shown in the following frequency distribution table. Which percentile is in the 26th position?
State your result/answer as value with exactly two digits after the decimal.
|
Values |
Frequency |
Cumulative |
|
4 |
2 |
2 |
|
5 |
5 |
7 |
|
6 |
7 |
14 |
|
7 |
11 |
25 |
|
8 |
16 |
41 |
|
9 |
6 |
47 |
|
10 |
4 |
51 |
|
25.00 |
||
|
50.00 |
||
|
26.00 |
||
|
50.98 |
||
|
25.50 |
In this problem, we have a cumulative frequency so we need to find the percentile is in 26th position is find using this following formula:
We need to find 50% percentile is given by,
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