Compute mean, median and mode for the following data : 31, 43, 67, 97, 57, 33, 42, 42, 43, 57, 34, 81, 42, 98, 42, 36, 90, 42, 60, 42, 37, 92, 64, 61, 51.

1. Mean

The mean, also known as the average, is calculated by summing up all the values in the dataset and dividing the total by the number of observations. To compute the mean for the given dataset:

Sum of all values = 31 + 43 + 67 + 97 + 57 + 33 + 42 + 42 + 43 + 57 + 34 + 81 + 42 + 98 + 42 + 36 + 90 + 42 + 60 + 42 + 37 + 92 + 64 + 61 + 51 = 1268

Number of observations = 25

Mean = Sum of all values / Number of observations = 1268 / 25 = 50.72

Therefore, the mean of the given dataset is 50.72.

2. Median

The median is the middle value of a dataset when it is arranged in ascending or descending order. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values. To compute the median for the given dataset:

Arranging the data in ascending order: 31, 33, 34, 36, 37, 42, 42, 42, 42, 42, 42, 43, 43, 51, 57, 57, 60, 61, 64, 67, 81, 90, 92, 97, 98

Number of observations = 25 (odd)

Median = Middle value = 42

Therefore, the median of the given dataset is 42.

3. Mode

The mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), two modes (bimodal), or more than two modes (multimodal). To compute the mode for the given dataset:

Counting the frequency of each value:

• 31: 1
• 33: 1
• 34: 1
• 36: 1
• 37: 1
• 42: 7
• 43: 2
• 51: 1
• 57: 2
• 60: 1
• 61: 1
• 64: 1
• 67: 1
• 81: 1
• 90: 1
• 92: 1
• 97: 1
• 98: 1

The value 42 appears most frequently with a frequency of 7 times.

Therefore, the mode of the given dataset is 42.

Conclusion

In summary, for the given dataset:

• Mean = 50.72
• Median = 42
• Mode = 42

These measures provide insights into the central tendency and typical value of the dataset, helping to understand its distribution and characteristics.