The weights (in pounds) of 10 patients are 180, 182, 184, 184, 185, 186, 188, 201,210, 214. Within what weight limits will 68% of the patients fall?

Question

The weights (in pounds) of 10 patients are 180, 182, 184, 184, 185, 186, 188, 201,210, 214.

Within what weight limits will 68% of the patients fall?

Answer 1

The 69% should ring a bell as one standard deviation from the mean (average). So we’re going to find four things:

1: the mean

2: the standard deviation (SD)

3: the mean - the SD

4: the mean + the SD

I’m assuming since you posted this that you must calculate it yourself! So the easy part is the mean

1: (180+182+184+184+185+186+188+201+210+214)/10 =191.4

2: to find the SD, there are four steps...

2a: subtract each value from the mean:

180-191.4=-11.4

182-191.4=-9.4

184-191.4=-7.4

184-191.4=-7.4

185-191.4=-6.4

186-191.4=-5.4

188-191.4=-3.4

201-191.4=9.6

210-191.4=18.6

214-191.4=22.6

2b: square each difference:

(-11.4)² =129.96

(-9.4)² =88.36

(-7.4)² =54.76

(-7.4)² =54.76

(-6.4)² =40.96

(-5.4)² =29.16

(-3.4)² =11.56

(9.6)² =92.16

(18.6)² =345.96

(22.6)² =510.76

**2c: find the mean (average) of all the squares

(129.96+88.36+54.76+54.76+40.96+29.16+11.56+92.16+345.96+510.76)/10 = 135.84

2d: find the square root of that

(135.84)^1/2= 11.66...

Phew!

3&4: so we have what we need to find the limits...

-11.66. Mean +11.66

lower limit <———— 191.4 ————> upper limit

191.4-11.66= 179.74 191.4+11.66=203.06

therefore, 68% of patients will fall between 179.74 and 203.06 lbs

**2c: if this is a sample and not the whole population, you’ll divide this number by 1 less than the count (so in this case, divide by 9 instead of 10) before you take the square root. Then follow the rest the same!

Good luck! I hope this helped.