Tag: range and mean deviation

The second quartile (Q2) is the median. First, sort the data: 10, 14, 15, 16, 18, 18, 18, 19, 20, 22, 23. With 11 observations, the median is the 6th value, which is 18.

The median (Md) divides the data into two halves (50%), the second quartile (Q2) is the median, the 5th decile (D5) is the median, and the 50th percentile (P50) is the median. Thus, Md = Q2 = D5 = P50.

Deciles divide data into 10 parts, so D3 represents 30% of the data. Percentiles divide data into 100 parts, so P30 also represents 30% of the data. Therefore, D3 = P30.

Given AM = (a+b)/2 = 6.5, so a+b = 13. Given GM = sqrt(ab) = 6, so ab = 36. The numbers 4 and 9 satisfy a+b = 13 and ab = 36.

The arithmetic mean is the sum of observations divided by the count. (10 + (-10)) / 2 = 0 / 2 = 0.

The sum of the first n natural numbers is n(n+1)/2. The average is the sum divided by n, which results in (n+1)/2.

By definition, the mode of a frequency distribution is the value that occurs most frequently, meaning it has the maximum frequency.

For a series with N observations, if N is odd, the median is the ((N+1)/2)th observation. Substituting N = 2n+1 gives ((2n+1+1)/2)th = (2n+2)/2 = (n+1)th observation.

Total runs in 4 innings = 4 * 32 = 128. Total runs needed for 5 innings = 5 * 50 = 250. Runs needed in 5th inning = 250 - 128 = 122.

In a moderately skewed distribution, the empirical relationship is: Mean - Mode = 3(Mean - Median). Given Mean = 10 and Mode = 7, we have 10 - 7 = 3(10 - Median), so 3 = 3(10 - Median), which means 1 = 10 - Median, so Median = 9.