Question

1. John's weight at his last five doctors' appointments has been 180 lbs, 170 lbs, 168 lbs, 184 lbs, and 182 lbs. What must John's

welght be at his next doctor's appointment to have a mean weight of 175 lbs?

Answer 1

`\boxed{166\: lbs \: [pounds \: of \: weight]}`

Explanation:

Mean =

Sum of data / # of data

Mean =

(180 lbs + 170 lbs + 168 lbs + 184 lbs + 182 lbs) / (5)

Since the weight of the next doctors appointment is unknown and must equal a mean weight of 175, there will be one more data point and we will let x represent this unknown weight:

175 lbs = (180 lbs + 170 lbs + 168 lbs + 184 lbs + 182 lbs + x lbs) / (5 + 1) →

175 lbs = (884 lbs + x lbs) / (6) →

(884 lbs + x lbs) / (6) = 175 lbs →

(884 lbs + x lbs) / (6) × 6 = 175 lbs × 6 →

884 lbs + x lbs = 1050 lbs →

(884 + x) lbs = (1050) lbs →

(884 + x = 1050) lbs →

(884 + x – 884 = 1050 – 884) lbs →

(x = 1050 – 884) lbs →

x = 166 lbs

_____________________________

166 lbs must be the weight for the mean of these weights to be 175 because:

(180 lbs + 170 lbs + 168 lbs + 184 lbs + 182 lbs + x lbs) / (5 + 1) →

(180 lbs + 170 lbs + 168 lbs + 184 lbs + 182 lbs + 166 lbs) / (5 + 1) →

(1050 lbs) / 6 →

175 lbs

Answer 2

166

Explanation:

1050-884=166

6x175=1050