Find the mean number of oranges kept in each basket. Which method of finding the mean did you choose? | Number of oranges | 10-14 | 15-19 | 20-24 | 25-29 | 30-34 | |---|---|---|---|---|---| | Number of baskets | 15 | 110 | 135 | 115 | 25 |
Answer (1)
To find the mean number of oranges kept in each basket, we will use the concept of finding the mean from a frequency distribution. We can follow these steps:
Identify the Midpoint of Each Class Interval : The midpoint is the number in the middle of each class range. It can be calculated by taking the average of the lower and upper boundaries of each class interval.
For 10-14: Midpoint = 2 10 + 14 = 12
For 15-19: Midpoint = 2 15 + 19 = 17
For 20-24: Midpoint = 2 20 + 24 = 22
For 25-29: Midpoint = 2 25 + 29 = 27
For 30-34: Midpoint = 2 30 + 34 = 32
Multiply the Midpoint by the Frequency : Multiply each midpoint by the number of baskets (frequency) for that interval.
For 10-14: 12 × 15 = 180
For 15-19: 17 × 110 = 1870
For 20-24: 22 × 135 = 2970
For 25-29: 27 × 115 = 3105
For 30-34: 32 × 25 = 800
Add the Results of All Interval Calculations : Calculate the sum of all these products to get the total number of oranges.
Total oranges = 180 + 1870 + 2970 + 3105 + 800 = 8925
Add the Frequencies : Sum all the frequencies to find the total number of baskets.
Total baskets = 15 + 110 + 135 + 115 + 25 = 400
Calculate the Mean : Divide the total number of oranges by the total number of baskets.
Mean = 400 8925 = 22.3125
Therefore, the mean number of oranges kept in each basket is approximately 22.31 .
