The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 17 of her matches, the bowler has taken 5 wickets each. The median number of wickets taken by the bowler in a match is __________ (rounded off to one decimal place).
Solving for the Median
Fundamental Concepts
- Median: The "middle" value in a sorted data set.
- Frequency: How many times a specific value occurs.
- Cumulative Frequency: The running total of frequencies. It helps us locate the middle position in a large data set without listing every single number.
Step 1: Create a Frequency Table
We extract the values from the bar graph and calculate the cumulative frequency (CF).
| Number of Wickets (x) | Frequency (f) | Cumulative Frequency (CF) |
|---|---|---|
| 0 | 5 | 5 |
| 1 | 7 | 12 |
| 2 | 8 | 20 |
| 3 | 25 | 45 |
| 4 | 20 | 65 |
| 5 | 17 | 82 |
| 6 | 8 | 90 |
| 7 | 4 | 94 |
| 8 | 3 | 97 |
| 9 | 2 | 99 |
| 10 | 1 | 100 |
Step 2: Determine Total Number of Data Points
Summing all frequencies gives us N = 100. Since N is even, the median is the average of the two middle terms.
Step 3: Find the Median Positions
For an even N, we look for the values at positions:
- Position 1: N / 2 = 50th match
- Position 2: (N / 2) + 1 = 51st match
Step 4: Locate the Values
Looking at our table:
- Up to the 45th match, the bowler has taken 3 wickets or fewer.
- From the 46th to the 65th match, the bowler has taken 4 wickets.
- Both the 50th and 51st values fall within this range.
Step 5: Final Calculation
Median = (Value at 50th + Value at 51st) / 2
Median = (4 + 4) / 2 = 4
Rounding to one decimal place as requested:
Median = 4.0