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Answer :
Answer:
Step-by-step explanation:Let's find the mode, mean, and median of the heights of 25 children:
Step 1: **Sorting the Heights**
Arrange the heights in ascending order:
\[ 160, 160, 160, 161, 162, 162, 162, 163, 163, 163, 163, 163, 163, 163, 163, 164, 164, 164, 164, 165, 165, 168 \]
Step 2: **Finding the Median**
Since there are 25 observations, the median is the average of the 12th and 13th values:
\[ \text{Median} = \frac{163 + 163}{2} = 163 \]
Step 3: **Finding the Mode**
The mode is the most frequently occurring height:
\[ \text{Mode} = 163 \]
Step 4: **Finding the Mean**
To find the mean, sum all the heights and divide by the number of observations (25):
\[ \text{Sum} = 160 \times 3 + 161 + 162 \times 3 + 163 \times 8 + 164 \times 4 + 165 \times 2 + 168 \]
\[ \text{Sum} = 480 + 161 + 486 + 1304 + 656 + 330 + 168 = 3485 \]
\[ \text{Mean} = \frac{3485}{25} = 139.4 \]
Step 5: **Conclusion**
- Mode of heights: \( \boxed{163} \)
- Median of heights: \( \boxed{163} \)
- Mean of heights: \( \boxed{139.4} \)
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Answer:
Step-by-step explanation:
The mode is the value that appears most frequently in the data. In this case, the value 163 appears 8 times, which is more than any other value. Therefore, the mode of the heights is:
163 cm
Mean:
To calculate the mean, we sum up all the values and divide by the number of data points:
Sum of heights = 168 + 165 + ... + 162 = 4051
Number of data points = 25
Mean height = Sum of heights / Number of data points = 4051 / 25 ≈ 162.04 cm
Median:
To find the median, we need to arrange the data in order (which it already is) and find the middle value. Since there are 25 data points (an odd number), the middle value is the 13th value:
Median height = 163 cm
So, the mode is 163 cm, the mean is approximately 162.04 cm, and the median is 163 cm.
