HOMEWORK #1 – SOLUTIONS Page 75 18) ordered data: 19, 20, 21, 22, 22, 23, 25, 30, 35, 35 n = 10 19 + 20 + 21++ 35 252
=
= 25.2
10
10
10 + 1
22 + 23
i=
= 5.5 ⇒ median =
= 22.5
2
2
x=
mode = 22, 35 20) ordered data: 154, 171, 173, 181, 184, 188, 203, 235, 240, 275 154 + 171+ 173 ++ 275 2004
=
= 200.4
10
10
10 + 1
184 + 188
i=
= 5.5 ⇒ median =
= 186
2
2
x=
no mode 24) x not possible; median not possible; mode = “watchful”; nominal data. Does not represent center of data. 28) ordered data: 1.0, 10.0, 15.0, 25.5, 31.5 n = 5 1+ 10 + 15 + 25.5 + 31.5 83
=
= 16.6
5
5
5 +1
i=
= 3 ⇒ median = 15
2
x=
no mode 58) ordered data for Car A: 28, 28, 30, 32, 34 n = 5 28 + 28 + 30 + 32 + 34 152
=
= 30.4 mpg
5
5
5 +1
i=
= 3 ⇒ median = 30 mpg
2
x=
mode = 28 mpg ordered data for Car B: 29, 29, 31, 31, 31 n = 5 29 + 29 + 31+ 31+ 31 151
=
= 30.2 mpg
5
5
median = 31 mpg
x=
mode = 31 mpg ordered data for Car C: 28, 29, 30, 32, 32 n = 5 28 + 29 + 30 + 32 + 32 151
=
= 30.2 mpg
5
5
median = 30 mpg
x=
mode = 32 mpg Car A should use the mean; Car B should use the median: Car C should use the mode. Page 92 4) range = 28‐7 = 21 ∑x
x=
12) s
2
i
13
= 18.3
2
2
2
28 − 18.3) + ( 25 − 18.3) ++ (16 − 18.3)
(
=
13 − 1
= 44.2 s = 44.2 = 6.7
n = 6, µ = 5, σ = 2
∑x
i
= 30; 2
x
−
5
(
)
∑ i
6
= 2 ⇒ ∑ ( xi − 5 ) = 24 ⇒
2
A solution is 3, 3, 3, 7, 7, 7 22) public school teachers: range = 39.9 ‐ 34.8 = 5.1 x = 37.375, s 2 = 2.953 ⇒ s = 1.72 private school teachers: range = 21.8 – 17.6 = 4.2 x = 19.5375, s 2 = 1.988, s = 1.41 There is more variation in public school teachers salaries. 30) x = 2400, s = 450
95% ⇒ x ± 2s ⇒ 2400 ± 2 ( 450 ) = 2400 ± 900 ⇒ ( $1500, $3300 )
48) a) b) c) d) x = 41.7, s = 6.0 x = 42.7, s = 6.0 x = 39.7, s = 6.0 Adding or subtracting a constant to the data changes the mean by that amount but does not change the standard deviation.