Mean and Median with Frequencies

Transcript

Mean and Median with FrequenciesLet’s say this is our data 13, 9, 2, 2, 3, 3, 3, 13, 5, 9, 9, 18, 10, 10, 13, 13, 13, 14, 14, 15, 18, 5, 9, 18 Now, we can write it in Frequency Table like Let’s find Mean and Median Finding Mean Now, Mean = (𝑆𝑢𝑚 𝑜𝑓 𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠)/(𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑂𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠) Since there are frequencies, we take those into account So, our Mean becomes Mean = (𝟐 × 𝟐 + 𝟑 × 𝟑 + 𝟓 × 𝟐 + 𝟗 × 𝟒 +𝟏𝟎 × 𝟐 + 𝟏𝟑 × 𝟓 + 𝟏𝟒 × 𝟐 + 𝟏𝟓 × 𝟏 + 𝟏𝟖 × 𝟑)/(𝟐 + 𝟑 + 𝟐 + 𝟒 + 𝟐 + 𝟓 + 𝟐 + 𝟏 + 𝟑) = 241/24 = 10.04 (approx.) Finding Median Median is the Middle most value Since frequencies are given, we find median by finding Cumulative Frequency Which means we add frequency of all previous values Since Total Number of Terms = 24 It is even Median would be the Mean of 12th and 13th term Since Cummulative frequency is 13 at Number 10, it means value of 12th and 13th position will be 10 So, Median = 10 We can check this by putting the numbers in ascending order and calculating 2, 2, 3, 3, 3, 5,5, 9,9,9,9,10,10,13,13,13,13,13,14,14,15,18,18,18