Question

describing the median-fit method

x	y		x	y
----	------		----	------
35	99.5		55	125
38	97.25		58	160
41	102		63	142
47	110.5		71	153
52	103.75

a restaurant manager records the number of tables seated (x) and the total number of cups of complimentary salsa (y) served. which statements show correct values for the median - fit method? check all that apply.

• the left summary point is (38, 97.25).
• the middle summary point is (52, 110.5).
• the right summary point is (63, 160).
• the slope of the line of best fit is 2.14.
• the y - intercept of the line of best fit is - 10.48.

Explanation:

Step1: Combine & sort data by x

Combine all (x,y) pairs: (35,99.5), (38,97.25), (41,102), (47,110.5), (52,103.75), (55,125), (58,160), (63,142), (71,153). They are already sorted by x.

Step2: Split into 3 equal groups

Group 1 (left): (35,99.5), (38,97.25), (41,102)
Group 2 (middle): (47,110.5), (52,103.75), (55,125)
Group 3 (right): (58,160), (63,142), (71,153)

Step3: Find median points for each group

Left median (x,y): (38, 97.25)
Middle median (x,y): (52, 110.5)
Right median (x,y): (63, 142)

Step4: Calculate slope of best fit

Slope uses left and right points:
$$m=\frac{142 - 97.25}{63 - 38}=\frac{44.75}{25}=1.79$$

Step5: Calculate y-intercept of best fit

Use left point $(38,97.25)$ in $y=mx+b$:
$$97.25=1.79\times38 + b$$
$$b=97.25 - 68.02=29.23$$

Step6: Verify each statement

1. Left summary point: Correct (matches Step3)
2. Middle summary point: Correct (matches Step3)
3. Right summary point: Incorrect (should be (63,142))
4. Slope: Incorrect (calculated as 1.79)
5. y-intercept: Incorrect (calculated as 29.23)

Answer:

• The left summary point is (38, 97.25).
• The middle summary point is (52, 110.5).