Question

what is your estimate for the measure of center you chose? question 3 for the 17 quiz scores graphed in the histogram, estimate the median.

Explanation:

Step1: Recall median definition

The median is the middle value of a dataset. For \( n = 17 \) (odd number of observations), the median is the \( \frac{n + 1}{2}=\frac{17+1}{2}=9^{\text{th}} \) value (when ordered from least to greatest). But here we use the histogram with quartiles (each 25%). The median is at the 50% mark. Looking at the histogram, the data is divided into four 25% sections. The median should be in the middle of the second 25% and third 25%? Wait, no—wait, the x - axis is calf girth (cm), but the question about quiz scores? Wait, maybe a typo, but the histogram has calf girth, but the question is about 17 quiz scores? Wait, maybe the histogram is for calf girth, but the key is: for a dataset, the median is the value where 50% of the data is below it. Looking at the histogram, the quartiles are marked: first 25% up to ~34, next 25% up to ~38? Wait, no, the graph has four 25% regions. Wait, the median (50th percentile) is between the 2nd and 3rd quartile? Wait, no, the median is the 50th percentile, so it's the middle of the data. Let's assume the histogram is symmetric or we estimate. Wait, the x - axis has values from 28 to 48. The median for a dataset with 17 values (or the histogram's data) – looking at the peaks, the middle range. Wait, the first 25% (left), then next 25%, then next 25%, then last 25% (right). The median is at the 50% mark, so between the 2nd and 3rd quartile? Wait, no, the median is the 50th percentile, so it's the value where half the data is below. Looking at the graph, the middle of the distribution. Let's see the x - axis labels: 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48. The median should be around the middle of the data. If we consider the quartiles (each 25%), the first 25% is left of ~34, next 25% up to ~38, then next 25% up to ~42? Wait, no, the graph's shaded regions: first 25% (left), then 25% (34 - 35), then 25% (36 - 38), then 25% (right). Wait, maybe the median is around 36 - 37? Wait, no, the question about quiz scores? Wait, maybe a mistake, but the histogram is for calf girth, but the key is to estimate the median. For a histogram, to estimate the median, we find the value where 50% of the area (frequency) is to the left. Let's count the number of data points. Wait, the y - axis is frequency (dots). Let's assume the total number of data points is such that each 25% is a quarter. If we take the median (50th percentile), it's in the middle of the second and third quartile? Wait, no, the median is the 50th percentile, so it's the value where cumulative frequency is 50%. Looking at the graph, the middle of the distribution is around 36 - 37? Wait, no, the x - axis at 36 - 37 has high frequency. Wait, maybe the median is around 36 or 37. But let's think again: for 17 data points, the median is the 9th value. If we order the data, the 9th value. Looking at the histogram, the first few values (28 - 33) have low frequency, then 34 - 35 have high, then 36 - 38, then lower. So the 9th value is likely around 36 - 37. But maybe the answer is around 36 or 37. Wait, the graph's x - axis: let's see the peaks. The middle of the data is around 36 - 37. So we estimate the median as 36 (or 37, but more likely 36 - 37). Wait, maybe the answer is 36 or 37. Let's check: if we have 17 data points, the median is the 9th. Let's count the frequency: from 28 - 33, how many? Let's say 28:1, 29:1, 30:2, 31:2, 32:2, 33:3 – that's 1 + 1+2 + 2+2 + 3 = 11? No, maybe not. Alternatively, the histogram is divided into four 25% sections. So the first 25% (25% of data) is left of, say, 34, next 25% up to 38, then next 25% up to 42, then last 25%. So the median (50%) is at the boundary between the second and third 25%? Wait, no, 25% + 25% = 50%, so the median is at the end of the second 25%? Wait, no, quartiles: Q1 is 25%, Q2 (median) is 50%, Q3 is 75%. So Q2 is the median. Looking at the graph, the second 25% is from ~34 to ~38, so the median is around 36 (middle of 34 - 38). So we estimate the median as 36 (or 37, but 36 is a good estimate).

Step2: Estimate from histogram

The histogram shows the data distribution, and the median (50th percentile) is in the middle of the data. By visually inspecting the graph, the central region (where 50% of the data lies) is around 36 cm (or similar, but based on the quartile divisions and the peak, 36 is a reasonable estimate).

Answer:

36 (or a value around 36 - 37, depending on visual estimation; 36 is a common estimate here)