Sure, let's find the mean, median, and mode of the runs scored by the 11 players step-by-step.
Given Data:
60, 15, 120, 50, 100, 80, 90, 89, 15, 70, 15
### Mean:
The mean is calculated by adding all the numbers together and then dividing by the number of data points.
Step 1: Sum of all runs scored.
[tex]\[ 60 + 15 + 120 + 50 + 100 + 80 + 90 + 89 + 15 + 70 + 15 \][/tex]
Step 2: Calculate the sum.
[tex]\[ 60 + 15 + 15 + 15 + 50 + 70 + 80 + 89 + 90 + 100 + 120 = 704 \][/tex]
Step 3: Divide the sum by the number of players (11).
[tex]\[ \text{Mean} = \frac{704}{11} = 64 \][/tex]
So, the mean is [tex]\(64\)[/tex].
### Median:
The median is the middle number in a sorted list of numbers. If the list has an even number of observations, the median is the average of the two middle numbers.
Step 1: Sort the runs scored in ascending order.
[tex]\[ 15, 15, 15, 50, 60, 70, 80, 89, 90, 100, 120 \][/tex]
Step 2: Find the middle number.
Since there are 11 players (an odd number of data points), the median is the 6th number in the sorted list.
The sorted list is:
[tex]\[ 15, 15, 15, 50, 60, 70, 80, 89, 90, 100, 120 \][/tex]
So, the median is:
[tex]\[ 70 \][/tex]
Thus, the median is [tex]\(70\)[/tex].
### Mode:
The mode is the number that appears most frequently in the data set.
Step 1: Identify the frequency of each run scored.
From the list:
[tex]\[ 15, 15, 15, 50, 60, 70, 80, 89, 90, 100, 120 \][/tex]
The number 15 appears 3 times, which is more than any other numbers.
So, the mode is [tex]\(15\)[/tex].
### Summary
- Mean: [tex]\(64\)[/tex]
- Median: [tex]\(70\)[/tex]
- Mode: [tex]\(15\)[/tex]
