1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sdas [7]
3 years ago
10

Various problems with data collection can cause some observations to be missing. Suppose a data set has 20 cases. Here are the v

alues of the variable x for 10 of these cases: 17, 6, 12, 14, 20, 23, 9, 12, 16, 21 The values for the other ten cases are missing. One way to deal with missing data is called imputation. The basic idea is that missing values are replaced, or imputed, with values that are based on an analysis of the data that are not missing. For a data set with a single variable, the usual choice of a value for imputation is the mean of the values that are not missing. (a) Compute the mean and standard deviation for the 10 cases for which x is not missing. (b) Create a new data set with 20 cases by using imputation where you set the values for the 10 missing cases equal to the mean that you computed in the previous part. Compute the mean and standard deviation for this new data set with 20 cases. (c) Summarize what you have learned about the possible effects of this type of imputation on the mean and the standard deviation.
Mathematics
1 answer:
mr Goodwill [35]3 years ago
4 0

Answer:

a) Mean= 15, standard deviation= 5.1575

b) Mean= 15, standard deviation= 3.6469

c) See below

Step-by-step explanation:

(a) Compute the mean and standard deviation for the 10 cases for which x is not missing.

The mean using the ten known values is

\bar x=\frac{17+6+12+14+20+23+9+12+16+21}{10}=15

The standard deviation is

\small s=\sqrt{\frac{(17-15)^2+(6-15)^2+(12-15)^2+(14-15)^2+(20-15)^2+(23-15)^2+(9-15)^2+(12-15)^2+(16-15)^2+(21-15)^2}{10}}=5.1575

(b) Create a new data set with 20 cases by using imputation where you set the values for the 10 missing cases equal to the mean that you computed in the previous part. Compute the mean and standard deviation for this new data set with 20 cases.

The new data set would be

17, 6, 12, 14, 20, 23, 9, 12, 16, 21, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15

The new mean for this set of values would be then

\bar x=\frac{\displaystyle\sum_{i=1}^{20}x_i}{20}=15

The new standard deviation is now

s=\sqrt{\frac{\displaystyle\sum_{i=1}^{20}(x_i-\bar x)^2}{20}}=3.6469

(c) Summarize what you have learned about the possible effects of this type of imputation on the mean and the standard deviation.

Obviously, this way of imputation is somewhat arbitrary and will produce a set of data undoubtedly skewed.  

It could possibly be a sensible way of imputing data if the amount of missing data is very little compared to the whole set, for example one or two data in a set of 100, but in this case we have 50% of missing data and it makes no sense this procedure.

You might be interested in
Find the quotient of 3/5 and 2/3
faltersainse [42]

Answer:

9/10

Step-by-step explanation:

Dividing by a fraction is the same as multiplying by that fraction's reciprocal (basically the fraction flipped).

\frac{3}{5} ÷ \frac{2}{3} = \frac{3}{5} *\frac{3}{2} =\frac{3*3}{5*2} =\frac{9}{10}

4 0
3 years ago
Read 2 more answers
A parabola passes through the points (–5, –10) and (5, –10), and the vertex is located at (0, 0). Find the equation of the parab
vitfil [10]
The equation of the parabola is -0.4x^2
8 0
3 years ago
Find the volume of a cone of radius 49cm and height 10cm​
den301095 [7]

Answer:

<h2> 25154.34{cm}^{3}</h2>

Step-by-step explanation:

Given,

Radius ( r ) = 49 cm

Height (h) = 10 cm

Volume of cone=?

Now,

Applying the formula to find the volume of cone:

\pi \:  {r}^{2}  \frac{h}{3}

Plugging the values,

\frac{22}{7}  \times  {49}^{2}  \times  \frac{10}{3}

\frac{22}{7} \times 2401 \times  \frac{10}{3}

Calculate

25153.34  \:  {cm}^{3}

Hope this helps...

Good luck on your assignment..

3 0
3 years ago
Read 2 more answers
What is the slope of a vertical line?<br>-1<br>0<br>1<br>unidentifed ​
kotykmax [81]
Any slope of a vertical line is infinite. it would be equivalent to x= -1 x=0 and x= 1. it will go on forever
3 0
2 years ago
What is the solution to the equation 9(x − 1) = 27? (1 point) x = 2.5 x = 0.5 x = −0.5 x = −3.5
Tems11 [23]

Step-by-step explanation:

Are you sure you wrote the answers correctly?

7 0
2 years ago
Read 2 more answers
Other questions:
  • A bag of mixed nuts contains cashews,
    8·1 answer
  • What is 8/40 in simplest form?
    8·2 answers
  • What's 2+2 I need help I'm on 2nd grade
    7·2 answers
  • 7x + 5=-2 find the value of 8x
    12·1 answer
  • Please help me thank you
    9·1 answer
  • The DeJeu family plan to drive to Marietta, GA to Newark, NJ. The distance is about 880 miles and the majority of their trip wil
    13·1 answer
  • What is the probability that a student who plays an instrument is in band
    12·1 answer
  • Which type of transformation is shown here?
    6·1 answer
  • THIS IS WORTH 50 POINTS I will mark you as the brainlyest only if you graph this on a GRAPH. Graph this on a GRAPH y= 1/3x+3 .
    13·2 answers
  • What is the total number of different 9-letter arrangements that can
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!