Representative Values

Transcript

Representative What is it? A single number that best shows what a whole group of numbers is like. Examples: Average (Mean): Sum / Count Middle Number (Median) Most Frequent (Mode) Why is it useful? Helps us understand data, make comparisons, and predict! Values When you have a big group of numbers, it's hard to talk about all of them at once. We use a Representative Value—one single number that represents the whole group. Let’s take a cricket example Cricket Example The runs scored by Shubman and Yashasvi in a cricket series are given in the table below. Who do you think performed better? Two friends Shreyas and Vaishanavi are discussing the scores. Vaishnavi’s view: She thinks Shubman is better because he has the highest single score (90). Shreyas’s view: He thinks Yashasvi is better because his total runs (175) are higher. Consistency: Yashasvi is more "consistent" because his scores are closer together, whereas Shubman had a 0 and then a 90. Second Series In the next series, their scores were The Problem: Shubman played 5 matches, but Yashasvi only played 4. If we just look at the Total, Shubman (110) looks better than Yashasvi (96). But is it fair? No, because Yashasvi didn't get a 5th chance! The Solution (The Mean): We can just calculate how much runs both of them scored per match - this is called the Average And, we calculate average by Average number of runs scored per match = (𝑻𝒐𝒕𝒂𝒍 𝒓𝒖𝒏𝒔)/(𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑴𝒂𝒕𝒄𝒉 𝒑𝒍𝒂𝒚𝒆𝒅) Now, Shubman’s Average: 110 ÷ 5 = 22 runs per match. Yashasvi’s Average: 9 ÷ 4 = 24 runs per match. Thus, we can conclude that On average, Yashasvi performed better even though his total was lower!