A company collected the ages from a random sample of its middle managers, with the resulting frequency distribution shown below. Class Interval Frequency 20 to < 25 25 to < 30 30 to < 35 35 to < 40 40 to < 45 45 to < 50 6 12 15 7 What is the midpoint of the third class interval?
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.
![A company collected the ages from a random sample of its middle managers, with the resulting frequency distribution shown below.
| Class Interval | Frequency |
|----------------|-----------|
| 20 to < 25 | 8 |
| 25 to < 30 | 6 |
| 30 to < 35 | 5 |
| 35 to < 40 | 12 |
| 40 to < 45 | 15 |
| 45 to < 50 | 7 |
What is the midpoint of the third class interval?
**Explanation:**
The table lists different age intervals (class intervals) and the corresponding number of middle managers (frequency) in each interval. The intervals are given in five-year ranges, starting from 20 to under 25 years, and so on.
To find the midpoint of the third class interval (30 to < 35):
- The formula for finding the midpoint of a class interval is:
\[ \text{Midpoint} = \frac{\text{Lower limit} + \text{Upper limit}}{2} \]
- For the third class interval (30 to < 35):
\[ \text{Midpoint} = \frac{30 + 35}{2} = 32.5 \]
Thus, the midpoint of the third class interval is 32.5 years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d109df6-2a29-4cf6-8621-5e28520611b8%2Fdd177894-db2d-46c2-bbe7-70398fb5d30c%2Ftt91pnk_processed.jpeg&w=3840&q=75)
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