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Ramakant Sharma
Ink Innovator
Asked: 2024-05-03T16:27:37+05:30 In:

Compute mean, median and mode for the following data : 31, 33, 37, 81, 92, 34, 31, 33, 31, 33, 37, 61, 32, 33, 72, 92, 72, 41, 33, 33, 94, 85, 45, 61, 51

For the following data: 31, 33, 37, 81, 92, 34, 31, 33, 31, 37, 61, 32, 33, 72, 92, 72, 41, 33, 33, 94, 85, 45, 61, 51, compute the mean, median, and mode.

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    1. Ink Innovator

      1. Introduction

      In this problem, we are given a set of data and tasked with computing the mean, median, and mode. Mean represents the average value, median represents the middle value when the data is arranged in ascending order, and mode represents the most frequently occurring value in the dataset. Let's calculate these statistical measures for the given data.

      2. Mean Calculation

      To calculate the mean, we sum up all the values in the dataset and divide the total by the number of values.

      Sum of all values = 31 + 33 + 37 + 81 + 92 + 34 + 31 + 33 + 31 + 33 + 37 + 61 + 32 + 33 + 72 + 92 + 72 + 41 + 33 + 33 + 94 + 85 + 45 + 61 + 51 = 1233

      Number of values = 25

      Mean = Sum of all values / Number of values
      = 1233 / 25
      = 49.32

      So, the mean of the given data is 49.32.

      3. Median Calculation

      To calculate the median, we first arrange the data in ascending order and then find the middle value. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.

      Arranging the data in ascending order:
      31, 31, 31, 32, 33, 33, 33, 33, 33, 34, 37, 37, 41, 45, 51, 61, 61, 72, 72, 81, 85, 92, 92, 94

      As there are 25 values, which is odd, the median is the middle value, which is the 13th value.

      Median = 37

      So, the median of the given data is 37.

      4. Mode Calculation

      To calculate the mode, we determine the value that appears most frequently in the dataset.

      Frequency of each value:
      31: 3 times
      33: 6 times
      37: 2 times
      81: 1 time
      92: 2 times
      34: 1 time
      61: 2 times
      32: 1 time
      72: 2 times
      41: 1 time
      94: 1 time
      85: 1 time
      45: 1 time
      51: 1 time

      The value 33 appears most frequently, 6 times.

      So, the mode of the given data is 33.

      5. Conclusion

      In conclusion, we have calculated the mean, median, and mode for the given dataset. The mean is 49.32, the median is 37, and the mode is 33. These statistical measures provide valuable insights into the central tendency and distribution of the data, helping us understand its characteristics and make informed decisions in data analysis and interpretation.

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