Question

a sample of 50 students was surveyed about their time spent in front of a screen (laptop, tablet, phone, etc.). each interval contains the left endpoint but not the right endpoint. in which interval is the median? 4,5) 5,6) 6,7) 7,8) hours of screen time per day

Explanation:

Step1: Calculate cumulative frequencies

From the histogram, frequencies for intervals are: [0,2) - 10, [2,3) - 5, [3,4) - 4, [4,5) - 5, [5,6) - 6, [6,7) - 5, [7,8) - 3, [8,9) - 2, [9,10) - 2, [10,11) - 2, [11,12) - 2. Cumulative frequencies: for [0,2) is 10; for [2,3) is 10 + 5=15; for [3,4) is 15 + 4 = 19; for [4,5) is 19+5 = 24; for [5,6) is 24 + 6=30; for [6,7) is 30+5 = 35; for [7,8) is 35 + 3=38; for [8,9) is 38+2 = 40; for [9,10) is 40+2 = 42; for [10,11) is 42+2 = 44; for [11,12) is 44+2 = 46.

Step2: Find the median interval

Since \(n = 50\), \(\frac{n}{2}=25\). The cumulative - frequency just greater than 25 is 30 which corresponds to the interval [5,6).

Answer:

[5,6)