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CA Foundation · Quantitative Aptitude · Statistical Description of Data

A company recorded the daily sales (in ₹ thousands) for 10 days: 85, 92, 88, 95, 87, 90, 88, 89, 91, 93. Which of the following statements about the distribution is correct?

After arranging the data and calculating mean (89.8) and median (89.5), we find these measures are extremely close. When the mean and median are nearly equal, the distribution is approximately symmetric. Skewness is assessed through the mean-median relationship, not by counting repetitions.

  1. AThe distribution is positively skewed because the mean exceeds the median
  2. BThe distribution is negatively skewed because three values are repeated or clustered
  3. CThe distribution is approximately symmetric because the mean and median are very closeCorrect
  4. DThe distribution cannot be described as either skewed or symmetric without calculating standard deviation

Explanation

Arrange data: 85, 87, 88, 88, 89, 90, 91, 92, 93, 95. Mean = (85+87+88+88+89+90+91+92+93+95)/10 = 898/10 = 89.8. Median = (89+90)/2 = 89.5 (average of 5th and 6th values for n=10). The mean (89.8) and median (89.5) are very close, indicating a symmetric or nearly symmetric distribution. Skewness is determined by the relationship between mean, median and mode—not by repetitions alone, and standard deviation measures spread, not shape.

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